First of all, if an element has order 11, then it means that x^11 = 1 (assuming that "1" is the identity in question), and that x^k is not equal to 1 for 1<k<11. You had the order switched.

Second of all, when you are calculating mod 5, all numbers (except 0) will have order at most 4, so I can't see how it makes sense to speak of order 11 when working mod 5.